In MEMS-based resonators (e.g., MEMS gyroscopes and other types of sensors) and other types of resonators, the magnitude of motion of a resonating body is a function of the drive force applied to induce the resonant motion of the resonating body, but is also a function of other forces, and can be described by an equation of motion. Typically, the resonating body is driven at resonance, in which case the velocity magnitude is such that the applied drive force is balanced by a mechanical damping force. Quality factor is an inverse measure of loss in the system. There are many sources of mechanical damping, none of which are very stable. Most sources are strong functions of temperature (e.g., thermoelastic damping, squeeze-film damping, etc.), though the sources do not necessarily have the same temperature dependence. Squeeze-film damping is also a strong function of ambient pressure, so a gyroscope packaged in a vacuum will often change behavior as the pressure inside the package changes, perhaps due to outgassing. Because the damping forces (quality factor) will change significantly due to environmental stresses, the resonator velocity amplitude is not stable. This can lead to a variety of system performance issues that can vary over time as the device is in use.
It is known to find the quality factor of a resonator by driving the resonator to its resonant frequency, and then observing the decay of the resonator's amplitude after terminating the drive forces. The resonator's amplitude will decay exponentially, and the time constant of that exponential decay can be used to determine the resonator's quality factor. Alternately, a resonator's quality factor may be determined by driving the resonator at a variety of frequencies and plotting the resonator's amplitude at each such frequency.